On some geometric properties of quasi-sum production models

A production function f is called quasi-sum if there are continuous strict monotone functions F , h 1 , … , h n with F > 0 such that f ( x ) = F ( h 1 ( x 1 ) + ⋯ + h n ( x n ) ) (cf. Aczél and Maksa (1996) [1]). A quasi-sum production function is called quasi-linear if at most one of F , h 1 , … , h n is a nonlinear function. For a production function f , the graph of f is called the production hypersurface of f . In this paper, we obtain a very simple necessary and sufficient condition for a quasi-sum production function f to be quasi-linear in terms of graph of f . Moreover, we completely classify quasi-sum production functions whose production hypersurfaces have vanishing Gauss–Kronecker curvature.